The long-term goal of this project is to construct a complete, quantitative picture of the transport and distribution of oxygen in skeletal and cardiac muscle for resting states, for exercise states, and for the transitions between them. This goal is to be achieved by combining theoretical results of this project with available experimental results. The theoretical results to be obtained are the specific aims of this project. The analyses to be carried out are divided into two categories: the oxygen transport path from red cell to mitochondrion, and experimental techniques used to measure oxygen distribution. The analyses of the transport path will include the following: oxygen release from red cells; oxygen transport from red cell membrane to sarcolemma; oxygen transport from sarcolemma to cytoplasm; oxygen transport from cytoplasm to mitochondrion; intercellular oxygen transport; time-dependent PO2 variations in rest-work transitions. The experimental situations to be analyzed include cell suspensions, and the freezing of working muscle. In addition, an analysis will be developed which will allow the measurement of the oxygen flux from a single capillary in working muscle. These analyses will be carried out by using a combination of asymptotic methods, such as matched asymptotic expansions, and both finite-difference and finite-element numerical methods. The work proposed here will lead to a better understanding of the factors which determine the distribution of oxygen in muscle. The analyses to be developed for normal tissue can be extended to deal with certain pathological cases, such as (1) oxygen release from sickle cells, (2) compromise of myoglobin-facilitated transport in cardiac muscle of smokers by carbon monoxide, and (3) oxygen delivery to cardiac muscle near an infarct.